Vector and trigonometric staticbalance computer



April 13, 1965 MccoY 3,178,108

VECTOR AND TRIGONOMETRIC STATIC-BALANCE COMPUTER Filed March 28, 1963 .2Sheets-Sheet l 1e '9 re W;

3 1 71K mum |7 |4 I3 7 I H' 2 INVENTOR Marlene McCoy ATTORNEY M. M COYTER April 13, 1965 VECTOR .2 Sheets-Sheet 2 Filed March 28, 1965INVENTOR ATTORNEY United States Patent 3,178,168 VECTOR ANDTRIGONOMETRIC STATIC- BALANCE COMPUTER Marlene McCoy, 5209 N. UniversityAve., Peoria, Ill.

- Fiied Mar. 28, 1963, Ser. No. 268,827

Claims. (Cl. 235-61) This invention relates to analog computers, and,more particularly, to devices for the rapid and ready summation ofvectors.

The study of vectors has been one of the most exasperating for manystudents. This is particularly true when several vectors are to beresolved into their components or are to be added. Since vectors areabstractions, they are apparently not readily understood by manyindividuals. Even the use of instruction aids has not fully solved thisproblem. And vectors are important in many activities and in many fieldsof endeavor. For this reason, computers have been devised to calculateand analyze vectors. Generally these computers are complex andcumbersome to use, and their value is questionable.

- This invention provides a new and simple device for the study and thecomputation of vector problems and trigonometric problems.

It is an object of this invention to provide a new and improved devicefor the study of vectors.

It is another object of this invention to provide a new and improveddevice for the computation of vector problems.

It is a further object of this invention to provide a new and improveddevice for the study and computation of trigonometric problems.

Other objects and advantages of this invention will become apparent asthe following description proceeds, which description should beconsidered together with the accompanying drawings in which:

FIG. 1 is a sectional view of the computer of this invention;

.FIG. 2 is a plan view of the computer of FIG. 1;

FIG. 3 is an illustration of a trigonometric problem to be solved by thecomputer of this invention;

FIG. 4 is a plan view of the chart of FIG. 2 showing the solution of theproblem of FIG. 3;

FIG. 5 is a diagram of a vector problem to be solved by the computer ofthis invention; and

FIG. 6 is a plan view of the chart of FIG. 2 showing the solution of theproblem of FIG. 5

Referring now to the drawings in detail, and in particu lar to FIGS. 1and 2, the reference character 11 designates a housing which may be madeof any suitable constructhe like. The housing 11 is generally circularin shape and shallow and contains a vertical support 12 in its center. Apivot pin 13 is vertically mounted in the top of the support 12 to fitin a conical bearing 14 in the center of a circular disc 15. Immediatelyabove the bearing 14 and centered on the top surface of the disc 15 is acircular bubble level. The housing 11 comprises a rim 17 at its topsurface, which is otherwise open. An annular disc 19 carrying a knob 18is supported on the rim 17 to be readily rotated thereon. The entireunit is adapted to be placed upon a level table top, desk or other suchsupporting surface.

It is important when the device of this invention is used, that the disc15 be statically balanced so that the bubble in the level 16 is centeredwhen the entire unit is supported in a level position prior to use. Thedisc 15 is calibrated in polar coordinates with two perpendicular centerlines XX and Y-Y indicating the horizontal and vertical axes. Inaddition, the angular distances starting at the right end of the XX axisare shown in degrees. To make the device easier to use, the angles in50. tron material such as wood, metal, synthetic resin, and

both directions are indicated. If desired, the values of the sine andthe cosine of the marked angles may also be shown. A plurality ofconcentric rings spaced equally from the center to the outer edge of thedisc 15 indicate the linear distance from the center out. Each of therings may be marked with a proportional value. Thus, for example, thefifth ring out from the center in a set of ten rings may be marked 5, or50, or 500. Each ring is thus labeled to indicate the relative distanceof that ring from the center of the disc 15. The outer annular disc 19is also divided into two sets of angular marks which indicate theangular distances from a zero point in either direction. When using thedevice of this invention, equal weights are placed at positions whichrepresent both the relative lengths of the vectors being calculated andtheir angular relationship. This can better be explained by reference tothe two problems shown in the drawings.

Considering first FIG. 3, a triangle ABC is shown with the lengths ofthe sides AB and AC being shown as 86 and 40 respectively. Angle B has avalue of 37. T determine the length of side BC and angles A and C, it isassumed that the side AB lies on the positive XX axis. A weight 23 isplaced on the X-X axis at a distance equivalent to 86, or approximately7 of the distance between the 8 and 9 circles on the disc 15. A secondweight 21, equal in size to the first weight 23, is placed on the disc15 along the radius which represents 37 in the second quadrant, or 37clockwise of the negative XX axis. The effect of the two weights 21 and23 is to unbalance the disc 15, causing it to tilt until its edge restson the rim 17. A third weight 22 is placed on the disc 15 on a linewhich approximately passes through the center 16 and the point at whichthe disc 15 rests on the rim 17. The weight 22 is then moved about untilthe disc 15 is completely balanced as shown by the bubble level 16. Thedistance of the weight 22 from the center, as indicated by theconcentric circles, indicates the length of the side CB. In this case itis about 60. The angle A is the angular distance between the negative XX axis and the radius on which the weight 22 rests. This isapproximately 23.75 (more correctly 23 40'). To determine the value ofangle C, the ring 19 is rotated until the angular value of the angle A,namely 23 40', lies on the radius of the line CA. Angle C is then thereading on the ring 19 which is adjacent the positive end of the XXaxis,

or the radius on which the side AB lies. This appears to beapproximately 119.25 or 119 15'. Of course, the disc 15 and the ring 19are not marked sufficiently well in the illustrative figures of thisapplication to provide the accuracy indicated. But with an instrumenthaving a large diameter and carefully measured markings, good accuracycan be expected.

The sides of triangles necessarily join to form a closed figure, but inthe solution of triangles with the instrument of this invention, thesides are represented as lengths of lines from the center of the disc15. For this reason, the supplement of the known angle is laid-off onthe disc 15. This is readily done if one of the sides is placed along amajor axis, as the XX axis. The supplementary angle is then the angulardistance from the other end of the same axis. The ring 19 is used todetermine the third angle of the triangle when two are already known.Thus, in the example given, the CA represents an angular distance of 37from the X-X axis. The aligning of the value of angle A with the line CAon disc 15 adds the values of the two angles A and B together andmeasures the total from one end of the X-X axis. The remaining angle Cis the difference between 180 and the sum of angles A and B and isindicated by the point at which the positive side of the XX axisintersects the ring 19.

In summing a plurality of vectors, a similar procedure is followed. FIG.5 represents a vector diagram in which the resultant vector is to bedetermined. Again, the vectors are related to the XX and the YY axes andthe angles are measured therefrom. In the diagram shown, the threevectors J, K, and L may represent forces being applied to a member whichlies at the center 0. The vector I represents a force having a value of10 pounds (or 10 tons) applied to the memberO at an angle with the +X--Xaxis of 30. The vector K represents a force having a strength of 20pounds applied to the member at an angle with the +YY axis of 30 or atan angle from the +X-X axis of 120. The third vector L represents aforce having a strength of pounds applied to the member 0 at an angle of45 from the XX axis or 225 from the +XX axis. Since .the forces vary bya ratio of two-to-one, the Weight representing the vector J is placed onthe 10 ring at an angle of 30 from the +X-X axis. The vector K isrepresented by two weights placed on the 10 ring at an angle of 120 fromthe +X-X axis. In this manner, the ratio of the forces is maintained,and the device is kept as sensitive as possible. The vector L isrepresented by one weight on the 10 ring at an angle of 225 from the+X-X axis. Again, the disc is unbalanced by the weights and tilts untilthe edge rests on the rim 17. The value of the resultant of the threevectors is found by using a pair of weights and moving them over thedisc 15 on the same general diameter defined by the center 0 and thepoint which rests on the rim 17 until the disc 15 is again balanced. Inthe example shown, one of the two weights is placed at the 10 ring andthe other at a position which is about 7.5 from the center, both on thesame radius which is at an angle of about 300 from the +X--X axis.Again, a larger diameter disc more carefully calibrated in smaller unitswill yield more accurate results.

From the above, it can be seen that the device of this inventiondemonstrates the effects of vectors upon a system and provides a simpleand effective device for calculating vector problems. In addition, theeffects of individual vectors, alone and with others, upon a system canbe demonstrated by the separate application of individual weights attheir proper locations on the disc 15. Therefore, the device of thisinvention is useful not only for calculation purposes, but also forteaching and demonstration purposes.

The above specification has described a new and improved device forcalculating the effects of vectors, vector summations, and manytrigonometric problems as well as for demonstrating these problems. Itis realized that the above disclosure may indicate to others differentways of utilizing the principles of this invention without .departingfrom the spirit thereof, and it is, therefore, intended that thisinvention be limited only by the scope of the appended claims.

What is claimed is:

1. A device demonstrating the computation of the vector sum of aplurality of vectors, said device comprising a housing open at one end,a vertically disposed support member centrally located in said housing,a pivot mounted upon the upper end of said support member, a frat discsupported upon said pivot in a balanced position, said disc beingcalibrated in distances from its pivot point and in angular distancesaround its circumference from a zero point, first weights of known valuein positions representative of vectors placed upon its upper surface inpositions which correspond to the size and direction of said vectors,second weights representative of the resultant and being of known value,said second weights being placed in positions to completely balance thecomposite etfect of said first weights, and means for indicating when abalance is achieved and the values and direct-ions of the resultant. V

2. A device for illustrating the computation of the value of a resultantof several vectors, said device comprising, a chart calibrated indistances from its center and in degrees displacement about itsperiphery, means for supporting said chart in a balanced position, firstbodies of known weight located on said chart in positions representativeof the sizes and directions of each of several vectors to unbalance saidchart, and means for indicating the value and direction of the forcenecessary to rebalance said chart.

3. A computer for computing trigonometric problems, said computercomprising, a chart having a point of static balance, said chart beingcalibrated in distances from said point of balance and angular distancesfrom a prescribed axis, means for supporting said chart at the point ofbalance, first weights of equal value positioned on said chart atpositions representative of the relative sizes and angular positions ofknown trigonometric quantities, second weights for rebalancing saidchart, and means for indicating when said chart is rebalanced afterbeing unbalanced by forces representative of trigonometric quantitiesapplied thereto.

4. The computer defined in claim 3 further comprising an annular scalecalibrated in degrees of arc and mounted concentric with said chart, andmeans for rotating said annular scale to indicate the summation oftrigonometric angles.

5. The computer defined in claim 3 further comprising means rotatablymounted concentric with said chart for indicating the difference betweenthe angular summation of the trigonometric quantities and a known valueof au-' gular measurement.

References Cited by the Examiner UNITED STATES PATENTS 2,364,026 11/44Lundgren 235-61 2,391,257 12/45 McWhorter 235-61.03 2,816,446 12/57Palmer 73-483 2,890,826 6/59 Cushman 235'--61.03 2,979,958 4/61 Kennedy73--48 3 LEO SMILOW, Primary Examiner.

w as,

1. A DEVICE DEMONSTRATION THE COMPUTATION OF THE VECTOR SUM OF APLURALITY OF VECTORS, SAID DEVICE COMPRISING A HOUSING OPEN AT ONE END,A VERTICALLY DISPOSED SUPPORT MEMBER CENTRALLY LOCATED IN SAID HOUSING,A PIVOT MOUNTED UPON THE UPPER END OF SAID SUPPORT MEMBER, A FLAT DISCSUPPORTED UPON SAID PIVOT IN A BALANCED POSITION, SAID DISC BEINGCALIBRATED IN DISTANCES FROM ITS PIVOT POINT AND IN ANGULAR DISTANCESAROUND ITS CIRCUMFERENCE FROM A ZERO POINT, FIRST WEIGHTS OF KNOWN VALUEIN POSITIONS REPRESENTATIVE OF VECTORS PLACED UPON ITS UPPER SURFACE INPOSITIONS WHICH CORRESPOND TO THE SIZE AND DIRECTION OF SAID VECTORS,SECOND WEIGHTS REPRESENTATIVE OF THE RESULTANT